Dong and Horvath
(2007) was the number 1 most highly viewed article of BMC Systems Biology in
2007. See archive.
It was also the number 4 most highly viewed article of all times (since the
creation of the journal, as of 05/25/20008).

Network concepts are increasingly used
in biology and genetics. For example, the clustering coefficient has been used
to understand network architecture; the connectivity (also known as degree) has
been used to screen for cancer targets; and the topological overlap matrix has
been used to define modules and to annotate genes. Dozens of potentially useful
network concepts are known from graph theory.

Results:

Here we study network concepts in
special types of networks, which we refer to as approximately factorizable
networks. In these networks, the pairwise connection strength (adjacency)
between 2 network nodes can be factored into node specific contributions, named
node `conformity'. The node conformity turns out to be highly related to the
connectivity. To provide a formalism for relating network concepts to each
other, we define three types of network concepts: fundamental-,
conformity-based-, and approximate conformity-based concepts. Fundamental
concepts include the standard definitions of connectivity, density,
centralization, heterogeneity, clustering coefficient, and topological overlap.
The approximate conformity-based analogs of fundamental network concepts have
several theoretical advantages. First, they allow one to derive simple
relationships between seemingly disparate networks concepts. For example, we
derive simple relationships between the clustering coefficient, the
heterogeneity, the density, the centralization, and the topological overlap. The
second advantage of approximate conformity-based network concepts is that they
allow one to show that fundamental network concepts can be approximated by
simple functions of the connectivity in
module networks.

Conclusions:

Using protein-protein interaction, gene
co-expression, and simulated data, we show that a) many networks comprised of
module nodes are approximately factorizable and b) in these types of networks,
simple relationships exist between seemingly disparate network concepts. Our
results are implemented in freely available R software code, which can be
downloaded from this webpage.